Dark-Halo Cusp: Asymptotic Convergence

We propose a model for how the buildup of dark halos by merging satellites produces a characteristic inner cusp, of a density profile \rho \prop r^-a with a -> a_as > 1, as seen in cosmological N-body simulations of hierarchical clustering scenarios. Dekel, Devor & Hetzroni (2003) argue that a flat core of a<1 exerts tidal compression which prevents local deposit of satellite material; the satellite sinks intact into the halo center thus causing a rapid steepening to a>1. Using merger N-body simulations, we learn that this cusp is stable under a sequence of mergers, and derive a practical tidal mass-transfer recipe in regions where the local slope of the halo profile is a>1. According to this recipe, the ratio of mean densities of halo and initial satellite within the tidal radius equals a given function psi(a), which is significantly smaller than unity (compared to being 1 according to crude resonance criteria) and is a decreasing function of a. This decrease makes the tidal mass transfer relatively more efficient at larger a, which means steepening when a is small and flattening when a is large, thus causing converges to a stable solution. Given this mass-transfer recipe, linear perturbation analysis, supported by toy simulations, shows that a sequence of cosmological mergers with homologous satellites slowly leads to a fixed-point cusp with an asymptotic slope a_as>1. The slope depends only weakly on the fluctuation power spectrum, in agreement with cosmological simulations. During a long interim period the profile has an NFW-like shape, with a cusp of 1<a<a_as. Thus, a cusp is enforced if enough compact satellite remnants make it intact into the inner halo. In order to maintain a flat core, satellites must be disrupted outside the core, possibly as a result of a modest puffing up due to baryonic feedback.Comment: 37 pages, Latex, aastex.cls, revised, ApJ, 588, in pres

A family of complex potentials with real spectrum

We consider a two-parameter non hermitean quantum-mechanical hamiltonian that is invariant under the combined effects of parity and time reversal transformation. Numerical investigation shows that for some values of the potential parameters the hamiltonian operator supports real eigenvalues and localized eigenfunctions. In contrast with other PT symmetric models, which require special integration paths in the complex plane, our model is integrable along a line parallel to the real axis.Comment: Six figures and four table

Harmonic oscillator well with a screened Coulombic core is quasi-exactly solvable

In the quantization scheme which weakens the hermiticity of a Hamiltonian to its mere PT invariance the superposition V(x) = x^2+ Ze^2/x of the harmonic and Coulomb potentials is defined at the purely imaginary effective charges (Ze^2=if) and regularized by a purely imaginary shift of x. This model is quasi-exactly solvable: We show that at each excited, (N+1)-st harmonic-oscillator energy E=2N+3 there exists not only the well known harmonic oscillator bound state (at the vanishing charge f=0) but also a normalizable (N+1)-plet of the further elementary Sturmian eigenstates \psi_n(x) at eigencharges f=f_n > 0, n = 0, 1, ..., N. Beyond the first few smallest multiplicities N we recommend their perturbative construction.Comment: 13 pages, Latex file, to appear in J. Phys. A: Math. Ge

A role for TSPO in mitochondrial Ca2+ homeostasis and redox stress signaling

The 18 kDa translocator protein TSPO localizes on the outer mitochondrial membrane (OMM). Systematically overexpressed at sites of neuroinflammation it is adopted as a biomarker of brain conditions. TSPO inhibits the autophagic removal of mitochondria by limiting PARK2-mediated mitochondrial ubiquitination via a peri-organelle accumulation of reactive oxygen species (ROS). Here we describe that TSPO deregulates mitochondrial Ca2+ signaling leading to a parallel increase in the cytosolic Ca2+ pools that activate the Ca2+-dependent NADPH oxidase (NOX) thereby increasing ROS. The inhibition of mitochondrial Ca2+ uptake by TSPO is a consequence of the phosphorylation of the voltage-dependent anion channel (VDAC1) by the protein kinase A (PKA), which is recruited to the mitochondria, in complex with the Acyl-CoA binding domain containing 3 (ACBD3). Notably, the neurotransmitter glutamate, which contributes neuronal toxicity in age-dependent conditions, triggers this TSPO-dependent mechanism of cell signaling leading to cellular demise. TSPO is therefore proposed as a novel OMM-based pathway to control intracellular Ca2+ dynamics and redox transients in neuronal cytotoxicity

The Equivalence Principle in the Non-baryonic Regime

We consider the empirical validity of the equivalence principle for non-baryonic matter. Working in the context of the TH\epsilon\mu formalism, we evaluate the constraints experiments place on parameters associated with violation of the equivalence principle (EVPs) over as wide a sector of the standard model as possible. Specific examples include new parameter constraints which arise from torsion balance experiments, gravitational red shift, variation of the fine structure constant, time-dilation measurements, and matter/antimatter experiments. We find several new bounds on EVPs in the leptonic and kaon sectors.Comment: 22 pages, late

Blind separation of speech signals based on lattice-ica geometric procedure

International audienc

The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions

We show how a proper use of the Lippmann–Schwinger equation simplifies the calculations to obtain scattering states for one dimensional systems perturbed by N Dirac delta equations. Here, we consider two situations. In the former, attractive Dirac deltas perturbed the free one dimensional Schrödinger Hamiltonian. We obtain explicit expressions for scattering and Gamow states. For completeness, we show that the method to obtain bound states use comparable formulas, although not based on the Lippmann–Schwinger equation. Then, the attractive N deltas perturbed the one dimensional Salpeter equation. We also obtain explicit expressions for the scattering wave functions. Here, we need regularisation techniques that we implement via heat kernel regularisation

The ABC Effect in Double-Pionic Nuclear Fusion and a pn Resonance as its Possible Origin

The ABC effect -- a long-standing puzzle in double-pionic fusion -- has been reexamined by the first exclusive and kinematically complete measurements of solid statistics for the fusion reactions $pn \to d\pi^0\pi^0$, $pd \to ^3$He$\pi\pi$ and $dd \to ^4$He$\pi\pi$ using the WASA detector, first at CELSIUS and recently at COSY -- the latter with a statistics increased by another two orders of magnitude. In all cases we observe a huge low-mass enhancement in the $\pi\pi$-invariant mass accompanied by a pronounced $\Delta\Delta$ excitation. For the most basic fusion reaction, the $pn \to d\pi^0\pi^0$ reaction, we observe in addition a very pronounced resonance-like energy dependence in the total cross section with a maximum 90 MeV below the $\Delta\Delta$ mass and a width of only 50 MeV, which is five times smaller than expected from a conventional $t$-channel $\Delta\Delta$ excitation. This reveals the ABC effect to be the consequence of a s-channel resonance with the formfactor of this dibaryonic state being reflected in the low-mass enhancement of the $\pi\pi$-invariant mass. From the fusion reactions to $^3$He and $^4$He we learn that this resonance is robust enough to survive even in nuclei.Comment: conference proceedings PANIC 0

Dynamics of a hyperbolic system that applies at the onset of the oscillatory instability

A real hyperbolic system is considered that applies near the onset of the oscillatory instability in large spatial domains. The validity of that system requires that some intermediate scales (large compared with the basic wavelength of the unstable modes but small compared with the size of the system) remain inhibited; that condition is analysed in some detail. The dynamics associated with the hyperbolic system is fully analysed to conclude that it is very simple if the coefficient of the cross-nonlinearity is such that , while the system exhibits increasing complexity (including period-doubling sequences, quasiperiodic transitions, crises) as the bifurcation parameter grows if ; if then the system behaves subcritically. Our results are seen to compare well, both qualitatively and quantitatively, with the experimentally obtained ones for the oscillatory instability of straight rolls in pure Rayleigh - Bénard convection

The N=4 string is the same as the N=2 string

We redo the quantization of the N=4 string, taking into account the reducibility of the constraints. The result is equivalent to the N=2 string, with critical dimension D=4 and signature (++--). The N=4 formulation has several advantages: the sigma-model field equations are implied classically, rather than by quantum/beta-function calculations; self-duality/chirality is one of the super-Virasoro constraints; SO(2,2) covariance is manifest. This reveals that the theory includes fermions, and is apparently spacetime supersymmetric.Comment: 7 pg (uuencoded dvi file; otherwise same as original